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According to A.A. Abrikosov in his paper on linear magnetoresistance, he makes a distinction between what he calls 'even' and 'odd' metals. In which he defines as:

  • Even metal: Number of electrons = Number of holes
  • Odd metal: Number of electrons =/= Number of holes

Has anyone else encountered such terms before? I would assume all pure metals to be 'even' (is there any reason for them not to?) and that Abrikosov is referring to doped metals when he is mentioning 'odd' metals..

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  • $\begingroup$ Why would you assume that all pure metals must be 'even' - given an actual 3D band structure one could easily have pockets of holes here and there. Even 'simple' metals can have very complex conduction processes. Under various conditions, Hall measurements in aluminum can show either positive or negative charge carriers. $\endgroup$
    – Jon Custer
    Commented Jan 5, 2017 at 14:11
  • $\begingroup$ I don't follow why having pockets of holes mean that there is an imbalance in holes and electrons. I was always under the impression that if there are holes, then there should be corresponding electrons elsewhere. Giving an overall net zero charge everywhere. Where would this pure metal get its extra charges from, if it is truly pure? $\endgroup$
    – Troy
    Commented Jan 5, 2017 at 14:19
  • $\begingroup$ Well, in a metal the concept of a 'hole' gets a little fuzzy (unlike a semiconductor where it is quite clear thermodynamically). So, in a metal, one can have portions of the 'valence' band above the Fermi level (although some might call this a semi-metal). One might call those 'holes'. Or you will have to better define what a 'hole' is in a metal. $\endgroup$
    – Jon Custer
    Commented Jan 5, 2017 at 14:22

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